The instant invention relates generally to the field of mathematical modeling and, more specifically, to models of planetary orbital systems used as research and teaching aids.
In many museums and planetariums, planetary motion is demonstrated by projecting a ball onto a hypersurface. A hypersurface is a three-dimensional sphere mapped into two-dimensional surfaces where surface area does not change. The hypersurface is somewhat conical in appearance. The model commonly seen at a museum uses a plastic mold shaped into a hypersurface. A ball is orbited around the hypersurface to simulate constant curvature in space, the hypersurface is presented as a fixed curvature and the ball orbits due to its presence. Due to the surface friction, the orbital path tends to decrease in radius. Eventually, the ball falls to the center of the hypersurface, thus ending the simulation. Although one can use this model to examine planetary orbits, the ball does not stay in orbit long enough to simulate actual planetary motion.